0.00/0.00	YES
0.00/0.00	
0.00/0.00	
0.00/0.00	Succeeded in reading "/export/starexec/sandbox2/benchmark/theBenchmark.trs".
0.00/0.00	    (CONDITIONTYPE ORIENTED)
0.00/0.00	    (VAR x y)
0.00/0.00	    (RULES
0.00/0.00	      f(x) -> x | x == a
0.00/0.00	      g(x) -> h(x,x)
0.00/0.00	      h(x,y) -> i(x)
0.00/0.00	    )
0.00/0.00	    (COMMENT [75] Example 39 submitted by: Thomas Sternagel and Aart Middeldorp)
0.00/0.00	
0.00/0.00	No "->="-rules.
0.00/0.00	
0.00/0.00	Decomposed conditions if possible.
0.00/0.00	    (CONDITIONTYPE ORIENTED)
0.00/0.00	    (VAR x y)
0.00/0.00	    (RULES
0.00/0.00	      f(x) -> x | x == a
0.00/0.00	      g(x) -> h(x,x)
0.00/0.00	      h(x,y) -> i(x)
0.00/0.00	    )
0.00/0.00	    (COMMENT [75] Example 39 submitted by: Thomas Sternagel and Aart Middeldorp)
0.00/0.00	
0.00/0.00	Removed infeasible rules as much as possible.
0.00/0.00	    (CONDITIONTYPE ORIENTED)
0.00/0.00	    (VAR x y)
0.00/0.00	    (RULES
0.00/0.00	      f(x) -> x | x == a
0.00/0.00	      g(x) -> h(x,x)
0.00/0.00	      h(x,y) -> i(x)
0.00/0.00	    )
0.00/0.00	    (COMMENT [75] Example 39 submitted by: Thomas Sternagel and Aart Middeldorp)
0.00/0.00	
0.00/0.00	Try to disprove confluence of the following (C)TRS:
0.00/0.00	    (CONDITIONTYPE ORIENTED)
0.00/0.00	    (VAR x y)
0.00/0.00	    (RULES
0.00/0.00	      f(x) -> x | x == a
0.00/0.00	      g(x) -> h(x,x)
0.00/0.00	      h(x,y) -> i(x)
0.00/0.00	    )
0.00/0.00	    (COMMENT [75] Example 39 submitted by: Thomas Sternagel and Aart Middeldorp)
0.00/0.00	
0.00/0.00	Failed either to apply SR and U for normal 1CTRSs to the above CTRS or to prove confluence of any converted TRSs.
0.00/0.00	
0.00/0.00	Try to apply SR and U for 3DCTRSs to the above CTRS.
0.00/0.00	
0.00/0.00	Succeeded in applying U for 3DCTRSs to the above CTRS.
0.00/0.00	U(R) =
0.00/0.00	    (VAR x1 x2)
0.00/0.00	    (RULES
0.00/0.00	      f(x1) -> u1(x1,x1)
0.00/0.00	      u1(a,x1) -> x1
0.00/0.00	      g(x1) -> h(x1,x1)
0.00/0.00	      h(x1,x2) -> i(x1)
0.00/0.00	    )
0.00/0.00	
0.00/0.00	U for 3DCTRSs is sound for the above CTRS.
0.00/0.00	
0.00/0.00	U(R) is confluent.
0.00/0.00	
0.00/0.00	YES
0.00/0.00	EOF